Structural preferential attachment: Stochastic process for the growth of scale-free, modular and self-similar systems

Abstract

Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment (SPA), a recently proposed growth principle for the emergence of the aforementioned properties. We study the corresponding stochastic process in terms of its time evolution, its asymptotic behavior and the scaling properties of its statistical steady state. Moreover, approximations are introduced to facilitate the modelling of real systems, mainly complex networks, using SPA. Finally, we investigate a particular behavior observed in the stochastic process, the peloton dynamics, and show how it predicts some features of real growing systems using prose samples as an example.

10 pages, 9 figures and 2 appendices

References in corpus (5)

• Modularity and community structure in networks
• Uncovering the overlapping community structure of complex networks in nature and society
• Hierarchical structure and the prediction of missing links in networks
• Structural preferential attachment: Network organization beyond the link
• Phase transition in the rich-get-richer mechanism due to finite-size effects

Cited by in corpus (7)

• Networks beyond pairwise interactions: structure and dynamics
• Phase transition in the recoverability of network history
• Simon's fundamental rich-get-richer model entails a dominant first-mover advantage
• Growing networks of overlapping communities with internal structure
• Complex networks as an emerging property of hierarchical preferential attachment
• Memory-cognizant generalization to Simon's random-copying neutral model
• On the constrained growth of complex critical systems